Low-rank image completion with entropy features

In this paper, we propose a novel method to complete the images or textures with the property of low rank. Our method leverages saliency detection with two entropy features to estimate initial corrupted regions. Then an iterative optimization model for low-rank and sparse errors recovery is designed to complete the corrupted images. Our iterative model can improve the initial corrupted regions and generate accurate and continuous corrupted regions via fully connected CRFs. By introducing a F-norm term in our model to absorb small noise, we can generate completed images which are more precise and have lower rank. Experiments indicate that our method introduces less local distortions than example-based methods for images with regular structures. It is also superior to the previous low-rank image completion method especially when the images contain low-rank corrupted regions. Furthermore, we show that the entropy features benefit the existing saliency detection methods too.     

TILT: Transform Invariant Low-Rank Textures

In this paper, we propose a new tool to efficiently extract a class of “low-rank textures” in a 3D scene from user-specified windows in 2D images despite significant corruptions and warping. The low-rank textures capture geometrically meaningful structures in an image, which encompass conventional local features such as edges and corners as well as many kinds of regular, symmetric patterns ubiquitous in urban environments and man-made objects. Our approach to finding these low-rank textures leverages the recent breakthroughs in convex optimization that enable robust recovery of a high-dimensional low-rank matrix despite gross sparse errors. In the case of planar regions with significant affine or projective deformation, our method can accurately recover both the intrinsic low-rank texture and the unknown transformation, and hence both the geometry and appearance of the associated planar region in 3D. Extensive experimental results demonstrate that this new technique works effectively for many regular and near-regular patterns or objects that are approximately low-rank, such as symmetrical patterns, building facades, printed text, and human faces.     

Joint weighted nuclear norm and total variation regularization for hyperspectral image denoising

A hyperspectral image is typically corrupted by multiple types of noise including Gaussian noise and impulse noise. On the other hand, a hyperspectral image possesses a high correlation in its spectral dimensions, and its Casorati matrix has a very low rank. Inspired by the recent development of robust principal component analysis, which can be used to remove sparse and arbitrarily large noise from a low-rank matrix, we propose a joint weighted nuclear norm and total variation regularization method to denoise a hyperspectral image data. First, weighted nuclear norm regularization is constructed for sparse noise removal. Total variation regularization is then imposed on each band of the hyperspectral image to further remove the Gaussian noise. A concrete optimization algorithm is developed to implement the two-stage regularization. The combined approach is expected to effectively denoise hyperspectral images even with varying data structures and under varying imaging conditions. Extensive experiments on both simulated and real data sets validate the performance of our proposed method.     

基于截断核范数低秩分解的自适应字典学习算法

针对过完备字典直接对图像进行稀疏表示不能很好地剔除高频噪声的影响,压缩感知后图像重构质量不高的问题,提出了基于截断核范数低秩分解的自适应字典学习算法。该算法首先利用截断核范数正则化低秩分解模型对图像矩阵低秩分解得到低秩部分和稀疏部分,其中低秩部分保留了图像的主要信息,稀疏部分主要包含高频噪声及部分物体轮廓信息;然后对图像低秩部分进行分块,依据图像块纹理复杂度对图像块进行分类;最后使用K奇异值分解（K-single value decomposition, K-SVD）字典学习算法,针对不同类别训练出多个不同大小的过完备字典。仿真结果表明,本文所提算法能够对图像进行较好的稀疏表示,并在很好地保持图像块特征一致性的同时显著提升图像重构质量。     

Linearized Alternating Direction Method with Adaptive Penalty and Warm Starts for Fast Solving Transform Invariant Low-Rank Textures

Transform invariant low-rank textures (TILT) is a novel and powerful tool that can effectively rectify a rich class of low-rank textures in 3D scenes from 2D images despite significant deformation and corruption. The existing algorithm for solving TILT is based on the alternating direction method. It suffers from high computational cost and is not theoretically guaranteed to converge to a correct solution to the inner loop. In this paper, we propose a novel algorithm to speed up solving TILT, with guaranteed convergence for the inner loop. Our method is based on the recently proposed linearized alternating direction method with adaptive penalty. To further reduce computation, warm starts are also introduced to initialize the variables better and cut the cost on singular value decomposition. Extensive experimental results on both synthetic and real data demonstrate that this new algorithm works much more efficiently and robustly than the existing algorithm. It could be at least five times faster than the previous method.     

基于生成对抗网络的低秩图像生成方法

低秩纹理结构是图像处理领域中具有重要几何意义的结构,通过提取低秩纹理可以对受到各种变换干扰的图像进行有效校正.针对受到各种变换干扰的低秩图像校正问题,利用生成式框架来缓解图像中不具明显低秩特性区域的校正结果不理想的问题,提出了一种非监督式的由图像生成图像的低秩纹理生成对抗网络（Low-rank generative adversarial network,LR-GAN）算法.首先,该算法将传统的无监督学习的低秩纹理映射算法（Transform invariant low-rank textures,TILT）作为引导加入到网络中来辅助判别器,使网络整体达到无监督学习的效果,并且使低秩对抗对在生成网络和判别网络上都能够学习到结构化的低秩表示.其次,为了保证生成的图像既有较高的图像质量又有相对较低的秩,同时考虑到低秩约束条件下的优化问题不易解决（NP难问题）,在经过一定阶段TILT的引导后,设计并加入了低秩梯度滤波层来逼近网络的低秩最优解.通过在MNIST,SVHN和FG-NET这三个数据集上的实验,并使用分类算法评估生成的低秩图像质量,结果表明,本文提出的LR-GAN算法均取得了较好的生成质量与识别效果.     

融合邻域回归和稀疏表示的图像超分辨率重构

对于图像超分辨率重建而言,通常会将图像的整体信息作为研究对象。然而图像本身含有的大量结构信息并没有得到充分利用。为了提高超分辨率重建的效果,实现对不同特征信息的利用,提出了一种融合邻域回归和稀疏表示的图像超分辨率重构算法。依据图像所具有的低秩性对高分辨率图像进行分解,获得高分辨率图像的低秩部分和稀疏部分;将对应的低分辨率图像与高分辨率图像的低秩部分和稀疏部分进行训练,学习得到对应的特征字典;基于高分辨率图像的低秩部分和稀疏部分分别基于稀疏表示和邻域嵌入进行高分辨率重构;基于低秩矩阵恢复理论,融合邻域回归和稀疏表示重构的高分辨率图像,得到最终的高分辨率图像。在测试集Set5和Set14上将提出的算法与几种经典算法进行对比实验,可视化和量化结果均表明,相比传统超分辨率算法,提出的算法在PSNR和SSIM都有很好的提升。     

基于约束的多样图纹理合成方法

基于已有的约束的多样图纹理合成算法,提出采用图像金字塔的方法来实现,并在其中利用了纹理的相关性原理,不仅可以合成自然纹理,而且对结构性较强的纹理也取得了较好的效果,合成速度也得到了提高。实验结果表明,该算法在合成质量和合成速度上都有较大的提高,对于控制某种纹理在合成结果图中的位置的纹理合成有广泛的适用性。     

Textile fabric defect detection based on low-rank representation

In this paper, we propose a novel and robust fabric defect detection method based on the low-rank representation (LRR) technique. Due to the repeated texture structure we model a defects-free fabric image as a low-rank structure. In addition, because defects, if exist, change only the texture of fabric locally, we model them with a sparse structure. Based on the above idea, we represent a fabric image into the sum of a low-rank matrix which expresses fabric texture and a sparse matrix which expresses defects. Then, the LRR method is applied to obtain the corresponding decomposition. Especially, in order to make better use of low-rank structure characteristics we propose LRREB (low-rank representation based on eigenvalue decomposition and blocked matrix) method to improve LRR. LRREB is implemented by dividing a image into some corresponding blocked matrices to reduce dimensions and applying eigen-value decomposition (EVD) on blocked matrix instead of singular value decomposition (SVD) on original fabric image, which improves the accuracy and efficiency. No training samples are required in our methods. Experimental results show that the proposed fabric defect detection method is feasible, effective, and simple to be employed.

     

Fast multi-scale joint bilateral texture upsampling

We present a new approach using a multi-scale joint bilateral filter for upsampling the synthesized texture generated by optimization-based methods. Our method is based on the following motivation: if the available exemplar texture is used as a priority to upsample the synthesized texture, a high resolution result that prevents image blurring can be obtained. Our multi-scale joint bilateral upsampling applies a spatial filter on each multi-scale layer of the synthesized texture, and jointly applies a similar range filter on exemplar texture, which guides the interpolation from low to high resolution, by magnifying and combining the upsampled information; the details of the upsampled texture are progressively enhanced, and the image blurring artifacts can be effectively avoided. We offer an accelerated joint bilateral filter, which enables our upsampling method to interactively generate a large texture. In addition, we propose a detail-aware texture optimization approach that incorporates image detail in texture optimization to improve the quality of the synthesized texture, on which the multi-scale joint bilateral filter works to generate a more convincing result. We show results for upsampling image and video textures and compare them to traditional upsampling methods, by this demonstrating that with low computational and memory costs, our method achieves better results.     

一种自适应组稀疏表示的图像修复方法

针对组稀疏表示图像修复方法采用固定大小的图像块,致使修复结果中存在纹理和结构清晰性较差的问题,提出一种基于自适应组稀疏表示的图像修复方法。由于自然图像中纹理和结构信息不同,为了与原方法固定图像块大小的组结构作区分,首先提出一种自适应选取样本图像块大小的方法来构造自适应的组结构;然后以组为单位对其进行奇异值分解,获得该图像块组的自适应学习字典,并利用分裂伯格曼迭代(Split Bregman Iteration)算法求解目标代价函数;最后通过调整组中的图像块数量和迭代次数对每个组的自适应字典和稀疏编码系数进行更新,以获取较好的修复效果。实验结果表明,该方法不仅在峰值信噪比和特征相似性度量上有所提高,同时也提高了修复效率。     

双重字典学习与自适应PCNN相结合的医学图像融合

目的 针对基于稀疏编码的医学图像融合方法存在的细节保存能力不足的问题,提出了一种基于卷积稀疏表示双重字典学习与自适应脉冲耦合神经网络（PCNN）的多模态医学图像融合方法。方法 首先通过已配准的训练图像去学习卷积稀疏与卷积低秩子字典,在两个字典下使用交替方向乘子法（ADMM）求得其卷积稀疏表示系数与卷积低秩表示系数,通过与对应的字典重构得到卷积稀疏与卷积低秩分量;然后利用改进的的拉普拉斯能量和（NSML）以及空间频率和（NMSF）去激励PCNN分别对卷积稀疏与卷积低秩分量进行融合;最后将融合后的卷积稀疏与卷积低秩分量进行组合得到最终的融合图像。结果 对灰度图像与彩色图像进行实验仿真并与其他融合方法进行比较,实验结果表明,所提出的融合方法在客观评估和视觉质量方面明显优于对比的6种方法,在4种指标上都有最优的表现;与6种多模态图像融合方法相比,3组实验平均标准差分别提高了7%、10%、5.2%;平均互信息分别提高了33.4%、10.9%、11.3%;平均空间频率分别提高了8.2%、9.6%、5.6%;平均边缘评价因子分别提高了16.9%、20.7%、21.6%。结论 与其他稀疏表示方法相比,有效提高了多模态医学图像融合的质量,更好地保留了源图像的细节信息,使融合图像的信息更加丰富,符合人眼的视觉特性,有效地辅助医生进行疾病诊断。     

结合全变差与自适应低秩正则化的图像压缩感知重构

针对基于固定变换基的协同稀疏图像压缩感知(CS)重构算法不能充分利用图像自相似特性的问题,提出了一种改进的联合全变差与自适应低秩正则化的压缩感知重构方法。首先,通过图像块匹配法寻找结构相似块,并组成非局部相似块组;然后,以非局部相似块组加权低秩逼近替代协同稀疏表示中的三维小波变换域滤波;最后,结合梯度稀疏与非局部相似块组低秩先验构成重构模型的正则化项,并采用交替方向乘子法求解实现图像重构。实验结果表明,相比协同稀疏压缩感知重构(RCoS)算法,该方法重构图像的峰值信噪比平均可提升约2 dB,所提算法在准确描述图像非局部自相似结构特征的前提下显著提高了重构质量,更好地保留了图像的纹理细节信息。     

Image restoration by matching gradient distributions

The restoration of a blurry or noisy image is commonly performed with a MAP estimator, which maximizes a posterior probability to reconstruct a clean image from a degraded image. A MAP estimator, when used with a sparse gradient image prior, reconstructs piecewise smooth images and typically removes textures that are important for visual realism. We present an alternative deconvolution method called iterative distribution reweighting (IDR) which imposes a global constraint on gradients so that a reconstructed image should have a gradient distribution similar to a reference distribution. In natural images, a reference distribution not only varies from one image to another, but also within an image depending on texture. We estimate a reference distribution directly from an input image for each texture segment. Our algorithm is able to restore rich mid-frequency textures. A large-scale user study supports the conclusion that our algorithm improves the visual realism of reconstructed images compared to those of MAP estimators.     

求解低秩矩阵融合高动态范围图像

目的 利用低秩矩阵恢复方法可从稀疏噪声污染的数据矩阵中提取出对齐且线性相关低秩图像的优点,提出一种新的基于低秩矩阵恢复理论的多曝光高动态范围（HDR）图像融合的方法,以提高HDR图像融合技术的抗噪声与去伪影的性能。方法 以部分奇异值（PSSV）作为优化目标函数,可构建通用的多曝光低动态范围（LDR）图像序列的HDR图像融合低秩数学模型。然后利用精确增广拉格朗日乘子法,求解输入的多曝光LDR图像序列的低秩矩阵,并借助交替方向乘子法对求解算法进行优化,对不同的奇异值设置自适应的惩罚因子,使得最优解尽量集中在最大奇异值的空间,从而得到对齐无噪声的场景完整光照信息,即HDR图像。结果 本文求解方法具有较好的收敛性,抗噪性能优于鲁棒主成分分析（RPCA）与PSSV方法,且能适用于多曝光LDR图像数据集较少的场合。通过对经典的Memorial Church与Arch多曝光LDR图像序列的HDR图像融合仿真结果表明,本文方法对噪声与伪影的抑制效果较为明显,图像细节丰富,基于感知一致性（PU）映射的峰值信噪比（PSNR）与结构相似度（SSIM）指标均优于对比方法：对于无噪声的Memorial Church图像序列,RPCA方法的PSNR、SSIM值分别为28.117 dB与0.935,而PSSV方法的分别为30.557 dB与0.959,本文方法的分别为32.550 dB与0.968。当为该图像序列添加均匀噪声后,RPCA方法的PSNR、SSIM值为28.115 dB与0.935,而PSSV方法的分别为30.579 dB与0.959,本文方法的为32.562 dB与0.967。结论 本文方法将多曝光HDR图像融合问题与低秩最优化理论结合,不仅可以在较少的数据量情况下以较低重构误差获取到HDR图像,还能有效去除动态场景伪影与噪声的干扰,提高融合图像的质量,具有更好的鲁棒性,适用于需要记录场景真实光线变化的场合。     

基于PSO的Wang Tiles纹理合成

如何在纹理样图中选择组成Wang Tiles的图像块决定着纹理的合成质量。基于PSO的Wang Tiles纹理合成通过粒子群优化算法在纹理样图中快速搜索边界差异最小的图像块,并用选取的图像块构建Wang Tiles,最后用Wang Tiles纹理合成算法合成纹理。实验表明,该算法合成的纹理具有较少的接缝,比随机选择图像块具有更好的合成效果。     

基于Criminisi的结构组稀疏表示图像修复算法

结构组稀疏表示(structural group sparse representation,SGSR)算法对结构组的估计值进行奇异值分解得到字典,然后用Split Bregman Iteration算法求解优化模型得到稀疏解,最后借助字典和稀疏解来修复图像。该算法在一定程度上解决了传统稀疏表示算法忽略图像块之间相似性导致重构图像的结构和纹理不够自然的问题。但该算法中,结构组的估计值采用双线性插值算法得到,因此对块状缺失图像的修复效果一般。为了更准确地计算结构组的估计值,提出用Criminisi算法代替双线性插值算法,并由此时的估计值生成更合理的字典和稀疏解,得到重构的结构组,进而更准确地修复图像。实验数据表明,与SGSR算法相比,所提出的算法在峰值信噪比和相似结构性指数上分别平均提高了2.66 dB和0.0017,且在结构和纹理上取得了更自然的主观视觉效果。     

基于低秩稀疏分解优化的图像标签完备

大量上传的网络图像因用户语义标注的随意性,造成了图像标签的不完备,大大降低了图像检索的效率.低秩稀疏是一种有效降低数据噪声的方法.为提高图像语义标签完备的准确度,提出一种基于低秩稀疏分解优化(LRSDO)的图像标签完备方法.首先结合待完备图像的视觉特征和语义搜索其近邻图像集;然后通过低秩稀疏分解模型获得其视觉特征与语义之间的映射关系,并以此预测该图像的候选标签;最后使用面向个体的标签共现频率方法对候选标签进行去噪优化,进而实现对其更加准确的自动图像标签完备.在基准数据集Corel5K和真实数据集Flickr30Concepts上进行了实验,结果表明,该方法在图像标签完备的平均准确率,平均召回率和覆盖率上均表现出更优的性能.     

改进稀疏表示算法在人脸识别中的应用

人脸识别的主要难度在于，受到光照变化、表情变化以及遮挡的影响，会使得采集的不同人的人脸图像具有相似性。为有效解决基于稀疏表示的分类算法（Sparse Representation-based Classification，SRC）在人脸训练样本不足时会导致识别率降低和稀疏表示求解效率较低的问题，提出了基于判别性低秩分解与快速稀疏表示分类（Low Rank Recovery Fast Sparse Representation-based Classification，LRR_FSRC）的人脸识别算法。利用低秩分解理论得到低秩恢复字典以及稀疏误差字典，结合低秩分解和结构不相干理论，训练出判别性低秩类字典和稀疏误差字典，并把它们结合作为测试时所用的字典；用坐标下降法来求解稀疏系数以提高了计算效率；根据重构误差实现测试样本的分类。在YALE和ORL数据库上的实验结果表明，提出的基于LRR_FSRC的人脸识别方法具有较高的识别率和计算效率。     

基于稀疏和低秩先验分离的快速动态MRI重建

为了加速动态核磁共振成像（MRI）的重建,并提取动态组织部分,提出一种基于将稀疏和低秩先验分离的重建方法。算法利用鲁棒主成分分析法（RPCA）,将动态MRI看作静态背景和动态组织的合成,建立相应的低秩矩阵和x-f域稀疏模型,再通过交替方向拉格朗日乘子法（ADMM）求解优化问题。与经典的k-t FOCUSS算法和k-t SLR算法进行对比,此算法能保证重建质量,即峰值信噪比（PSNR）、结构相似性（SSIM）等评价指标。实验结果表明,该算法能实现快速动态MRI的成像,减少运动伪影,同时更利于提取动态信息。